Marked-to-Market Interest Rate Swaps: A Solution to the Interest Rate Risk Management Problem of Indebted Developing Countries
  • 1 0000000404811396 Monetary Fund


Indebted developing countries have been prevented from hedging their exposure to volatility in short-term international interest rates by a lack of creditworthiness, a shortage of international reserves, and a lack of financial expertise. This paper uses the conventional interest rate swap contract—a contract between two parties to exchange a fixed payment stream for a floating payment stream without an exchange of principal—to construct an interest rate risk management tool that can overcome these difficulties. The proposed swap contract aims to reduce the credit risk borne by the counterparty in the swap transactions by shortening the performance period of the country through periodic resettlement of capital gains and losses on the existing swap contract combined with a recontracting at the prevailing market swap rate.

INDEBTED DEVELOPING COUNTRIES have been prevented from hedging their exposure to volatility in short-term international interest rates by a lack of creditworthiness, a shortage of international reserves, and a lack of financial expertise. This paper develops a risk management technique aimed at overcoming these difficulties.

The past ten years have seen a historically high volatility of financial yields. This development has led to increased emphasis on managing financial risk, that is, the risk of loss arising from open financial positions. Such open positions arise largely in the form of mismatched receipts and payments, as might occur in indebted developing countries, for example, when short-term financing is used for longer-term investment or when receipts and payments are denominated in different currencies. Financial risk assumes an added dimension when the country faces the possibility of illiquidity or default in the event of unfavorable movements in interest or exchange rates.

Active risk management has become an important element of financial management in most industrial countries. Efforts to deal with increased volatility of financial yields has led participants in the major financial markets to resort to the use of a large variety of hedging instruments and techniques. Most notable in this regard has been the increased use of financial contingent contracts, such as financial futures, forward, and options contracts, and such new contracts as interest rate and exchange rate swaps.1 In some instances the underlying market value of trades in these contracts has come to exceed that of the underlying instruments.2

Indebted developing countries have been particularly adversely affected by the increased volatility of financial yields. First, the interest charges on external obligations of developing countries, which frequently constitute a large fraction of their external financing requirement, are indexed to short-term international interest rates, such as three- or six-month LIBOR or U.S. Treasury bill rates.3 Since the timing and magnitude of variations in terms of trade or in receipts from investment projects have not generally coincided with variations in short-term index rates, the indebted developing countries have experienced a significant increase in financial risk.

Second, a lack of creditworthiness and of international reserves, as well as a lack of financial expertise, have severely limited the choice of risk-management instruments and techniques available to such countries. Indebted developing countries, particularly those with rescheduled debt, have generally been unable to refinance their floating-rate debt in the international fixed-rate debt markets.4 The countries have, therefore, been limited to hedging their interest rate exposure in the derivative markets.5 Considerations of creditworthiness have denied indebted developing countries the use of forward interest rate contracts, such as forward rate agreements and interest rate swaps. Such contingent contracts generally require the indebted developing country to make unsecured payments on future dates and hence contain an element of credit risk. Furthermore, the lack of foreign exchange has limited the use of options contracts, such as interest rate caps, the purchase of which requires payment of an up-front premium. Such options entitle the country to receive payments should interest rates rise above a predetermined level. Finally, although the use of exchange-traded financial futures, such as the LIBOR futures contract, has not been much hampered by consideration of creditworthiness, which has been minimized through certain institutional arrangements, nor by lack of foreign exchange resources, it has nevertheless been severely restrained by the unavailability of liquid futures contracts with delivery dates extending into the medium term, that is, from 18 to 60 months. The absence of a sufficiently liquid market for medium-term futures contracts makes it necessary to sell and buy actively short-term futures to approximate the results of a medium-term hedge6 through a stacking or sequencing of short-term contracts. The requisite financial expertise and the mechanisms to monitor delegated trading authority required for the management of the short-term futures positions designed for medium-term interest rate hedges are not yet readily available in most indebted developing countries. Furthermore, it is doubtful that the institutional framework necessary to support the acquisition and growth of such financial expertise can be created in the near future.

Thus, although most of the interest cost of the external obligations of indebted developing countries are tied to increasingly volatile short-term international interest rates, such countries have not been able to undertake active medium-term interest rate risk management, despite the benefits that greater interest rate certainty would have for the implementation of medium-term adjustment programs or debt rescheduling agreements undertaken by indebted developing countries.7

This paper uses the conventional interest rate swap contract—a contract between two parties to exchange a fixed payment stream for a floating payment stream without an exchange of principal—to construct an interest rate risk management tool that can overcome a lack of creditworthiness and a lack of international reserves without making undue demands on the financial expertise of such countries. The proposed contract is designed to open up to indebted developing countries the possibility of achieving a period of desired length during which interest rates on external obligations remain fixed. It achieves this aim by reducing the credit risk borne by the counterparty in the swap transactions. This reduction is accomplished by shortening the performance period of the country through periodic resettlement of capital gains and losses on the existing swap contract combined with a recontracting at the prevailing market swap rate.8 Furthermore, since interest rate swap contracts extend into the medium-term without requiring active management or an initial premium outlay, it is possible to avoid the problems associated with the lack of international reserves and of financial expertise. As is the case with futures contracts, however, the resettlement mechanism, while not demanding an increase in total cash outlays in present value terms, nevertheless requires cash-flow management over the period of the swap contract.

The great depth and liquidity of the interest rate swap market, estimated at $1.5 trillion of notional principal outstanding,9 would comfortably permit a large-scale use of the proposed swap contract by indebted developing countries if the solutions to the various technical problem advanced in this paper are accepted by market participants.

Section I of this paper discusses the factors that prevent indebted developing countries from making more extensive use of the conventional interest hedging risk instruments (futures and forward contracts, conventional swap contracts, and options contracts). Section II discusses the proposed risk management instrument and its intended use. Section III addresses some additional problems and summarizes the paper.

I. Impediments to Market-Based Interest Rate Risk Management by Indebted Developing Countries

Although it is generally recognized that active management of interest rate risk by indebted developing countries can reduce, inter alia, the threat to financial planning posed by higher volatility of short-term international interest rates, the use of market-based risk management has not become part of the financial policy of such countries.10 This section points the way toward the design of an improved risk management tool for indebted developing countries by identifying the causes of their inability to make use of the existing instruments. Interest rate risk management tools that have been applied successfully and have stood the test of time can be classified into five broad categories: (1) choosing an optimal period during which interest payments remain fixed by refinancing floating-rate debt with fixed-rate debt in primary debt markets; (2) entering into interest rate forward contracts ; (3) entering into interest rate swap agreements ; (4) purchase of interest rate options ; and (5) purchase or sale of interest rate futures contracts. The inability of indebted developing countries to make significant use of any of these five methods of reducing their exposure to short-term international interest rates has been attributable to lack of creditworthiness, lack of international reserves, and a lack of financial expertise.

Concern about the creditworthiness of indebted developing countries, particularly countries with rescheduled debt, has meant that such countries do not generally have access to the fixed-interest rate debt markets and thus are denied the possibility of lowering their exposure to volatile international interest rates through a lengthening of coupon periods.11 Instead, 80 percent of the external obligations of developing countries carry a coupon period of six months or less. Their inability to alter the coupon period of existing debt directly forces indebted developing countries to do so indirectly through the use of derivative markets (forwards, futures, options, and swaps).

Considerations pertaining to the creditworthiness of indebted developing countries, many with rescheduled debt, have also made markets for interest rate forward contracts inaccessible to such countries. Interest rate forward contracts—contracts for the delivery of funds at a specified future date and interest rate—are pure credit instruments in that they expose counterparties to the risk of loss should the country renege on its payment obligations during the life of the contract.12 For example, in order to offset a rise in the six-month LIBOR index rate at the next interest rate reset date of its external obligations, a debtor country could enter a forward rate agreement (FRA) for delivery of six-month funds at the reset date at a specified interest rate. If, under these circumstances, the six-month LIBOR at the delivery date is below the rate specified in the FRA, then the country owes interest payments to its counterparty in the FRA. Hence the counterparty is exposed to credit risk if rates fall. The longer the performance period, that is, the length of the forward contract, and the more volatile the interest rate of the underlying instrument, the greater the credit risk in forward contracts.13 Such credit risk in forward interest rate contracts has meant that their use is largely confined to interbank markets.

The presence of counterparty risk has also resulted in the exclusion of indebted developing countries from the interest rate swap market. An interest rate swap is an agreement among two parties to exchange a stream of fixed interest payments for a stream of floating interest payments over a specified period without exchanging any principal payments. For example, the developing country would undertake to make fixed interest rate payments at a specified rate on a notional principal during a specified period, while the counterparty would make floating interest payments on the same notional principal. Since the country commits itself in the interest rate swap agreement to make unsecured future payments at regular settlement dates, up to a specified maturity date, the counterparty incurs credit risk. For example, a default on the fixed interest payments14 by the country exposes the floating-rate payor to losses if fixed rates have declined since the beginning of the swap contract. Thus the swap participant’s credit risk exposure depends on the potential movement of interest rates over the period of the swap and on the likelihood of a performance failure by the swap counterparty.

The lack of sufficient foreign exchange reserves has prevented indebted developing countries from purchasing interest rate caps. Such interest rate options have become an important and successful interest rate risk management tool, one whose use is not affected by the credit risk of the purchase of the cap. A floating-rate borrower, such as an indebted developing country, can obtain medium-term protection against an increase in the index rate by purchasing an interest rate cap. The market for caps is judged sufficiently deep and liquid to accommodate substantial participation by indebted countries.15 Caps are sold by major commercial banks and securities houses. The main drawback of using interest rate caps to manage rate volatility is that the purchase of caps requires a fee, whose size is determined by the level at which the index rate is capped, the length of time over which the cap is in effect, and the expected volatility of the capped rate.16 For example, the estimated cost of capping LIBOR 50 basis points above its current value for the next three years is about 141 basis points of the principal amount (see Table 1). Offsetting this price disadvantage is that, while caps limit upward movements, they do not deprive the country of the benefits of downward movements in rates. Indebted developing countries have, however, generally been unable or unwilling to use scarce foreign exchange resources for the interest rate caps. Since the indebted developing country does not incur obligations to make payments at future dates, the creditworthiness of such countries is not an impediment to the use of interest rate caps.

Table 1.

Premia for Interest Rate Caps on Three-Month LIBOR in January 19891

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These premia are an average of premia quoted by major banks and securities houses in New York in January 1989. The three-month LIBOR averaged 9.5 percent during this period.

An important interest rate hedging instrument not affected by creditworthiness considerations or by lack of foreign exchange reserves is the exchange-traded interest rate futures contract. Such futures contracts are promises to deliver a particular financial asset at a predetermined price at a specified date in the future. The terms and the delivery dates of the contract are standardized as are the procedures for trading the contract. Furthermore, certain institutional arrangements, to be discussed below, serve to eliminate credit risk from the contract. The main shortcoming of using futures contracts to reduce the impact of interest rate volatility over the medium term is their relatively short time horizon, which limits its usefulness to indebted developing countries. The Eurodollar futures contract, which represents an obligation on the part of the holder of the contract to buy and represents an obligation on the part of the writer of the contract to sell at a predetermined price, on a specified future date, a Eurodollar time deposit of three- or six-month maturity, is the most successful of such contracts.17 Sales of Eurodollar futures contracts can be used to lock in a forward LIBOR rate for some future date. Any increase in LIBOR will then be offset by profits on the country’s short position in Eurodollar futures, while the benefits of a decline in LIBOR would be negated by corresponding losses on the contracts.

The market in the contracts for delivery of three-month Eurodollars up to one year is most liquid and is thought able to accommodate substantial participation by indebted developing countries. However, the markets for longer-dated contracts or for contracts for future delivery of six-month or one-year Eurodollars are not sufficiently liquid to accommodate substantial participation by indebted developing countries. Hence, the hedger has to employ a sequence (strip) or a stack of three-month contracts if he desires to lock in interest rates for periods in excess of one year.18 Interest rate hedging with the liquid three-month Eurodollar futures contract beyond 12 months is, therefore, not generally fully effective.

In addition, the hedging of interest rates risk beyond the immediate future with shorter term financial futures requires continuous adjustment in contract positions. Such activity requires skilled personnel capable of dealing in wholesale hedging markets on a continuous basis. While these risk management services can to some extent be purchased from various financial institutions, even the evaluation of the quality and cost of these services requires considerable knowledge of market instruments and techniques. A further problem arises in designing and implementing an internal control mechanism that effectively limits the activities of risk managers to legitimate hedging operations. Recent experience in some prominent financial firms has shown that potentially large trading losses are possible if internal controls are inadequate. For this reason indebted developing countries have been slow to use this instrument for hedging interest rate risk over the medium term.

In contrast to the interest rate cap, futures contracts can be entered into by a country without a payment of an up-front premium. However, while in the former case the countries can still benefit from a decline in rates, a futures contract locks in a fixed interest rate. The greatest impediment to the use of the interest rate futures markets is, however, the limitation of the potential length of the hedge.

The discussion above thus shows that considerations of creditworthiness have closed access of indebted developing countries to fixed-rate debt markets, forward markets, and interest rate swap markets,19 while the requirement of up-front premia deter the use of the interest rate options market. Finally, limitations on the feasible length of the hedge, and considerations pertaining to managing and monitoring futures positions have limited the usefulness of interest rate futures as a medium-term risk management tool for indebted developing countries.

II. The Marked-to-Market Interest Rate Swap Contract

The discussion in the previous section underscores the fact that the special circumstances of indebted developing countries, particularly those with rescheduled debt, require an interest rate risk management tool that must satisfy a number of conditions before it can successfully be used to manage the interest rate risk facing such countries. First, the access of indebted developing countries to the risk-management tool should not be influenced by the markets’ perception of the creditworthiness of the country. Second, the instrument should provide cover over the medium term, that is, from two to five years. In that case, it would add certainty to medium-term financial programs, as well as smooth cyclical movements in interest rates, enabling the indebted developing country to extend the coupon period on their external obligations from the conventional six months into the medium term. Third, the use of the risk management instrument should not require a large up-front fee. Instead, it is assumed that the indebted country is prepared to trade the benefits of downward flexibility of the rate to be hedged for limits on the upward movement of interest rates. Fourth, the risk management product must be easy to use and not require active management of positions or monitoring of delegated trading activity. Fifth, the market for the risk management product must be sufficiently deep to allow large-scale participation by indebted developing countries.

From the discussion of the previous section, it is apparent that none of the existing risk management products simultaneously satisfies these five requirements. Our strategy in the search for an interest rate hedge for use by indebted developing countries is to assume that it is not possible to design a new instrument that will gain sufficient market acceptance to provide the depth and liquidity necessary to allow indebted developing countries to hedge a significant part of their external floating-rate obligation. Furthermore, we also assume that it is not possible to improve the depth and liquidity of the longer-dated financial futures and forward contracts sufficiently to satisfy the medium-term hedging needs of indebted developing countries. Lastly, we rule out the possibility of external financial assistance for developing countries for the purchase of interest rate cap products.

By elimination, these assumptions point toward the interest rate swap contract as the only candidate for use in managing interest rate volatility. The swap market possesses the necessary depth over the medium-term hedging horizon to accommodate substantial participation by indebted developing countries. Furthermore, entering into a medium-term swap contract does not require an up-front premium and can be done in a single transaction without a need for continuous monitoring. As was the case with forward rate markets, however, indebted developing countries do not enjoy access to the swap market because of the reluctance of market participants to expose themselves to the greater performance risks of such countries over a medium-term performance period. We conclude, therefore, that the only feasible solution to the interest rate risk management problem of the group of indebted developing countries is to modify the conventional swap contract to reduce or eliminate the risk of nonperformance from the conventional interest rate swap contract. In doing so, we shall take our cue from the futures markets in which certain institutional features have been employed to eliminate credit risk from the futures contract.

Conventional Interest Rate Swap

The conventional interest rate swap has become one of the most successful instruments for interest rate risk management.20 In an interest rate swap the indebted developing country would pay a stream of fixed rate interest payments and receive a stream of floating rate payments over an agreed time period. The counterparty, usually a bank, would receive fixed and would pay floating. No actual principal would be exchanged either at the beginning or at the termination of the contract.21 For example, at current swap rates, the country would have to pay a fixed 9.5 percent on a notional principal of, say, $100 million for five years and receive six-month LIBOR payments based on the same notional principal. A floating-rate borrower can thus achieve any desired medium-term lengthening of his interest rate period through the use of an interest rate swap. Although the market is an over-the-counter market, a significant amount of standardization in swap contracts and procedures has added greatly to liquidity in this market. Bid-ask spreads tend to be narrow, and maturities go out to 20 years, with most liquidity occurring within the three-to-ten year range. Money center banks have generally acted as counterparties in well over 80 percent of all interest rate swaps.

Credit Risk in Swap Contracts

The credit risk of a swap contract with an indebted developing country at time t would be equal to the loss incurred by the counterparty when the country defaults on its fixed interest payments at time t. Assume c is the fixed interest coupon payable on a notional principal for a T period swap at the beginning of period 1. If the fixed rate for a T-1 period swap at the beginning of period 2 is also quoted as c, then either counterparty can replace the original swap agreed to at the beginning of period 1 with a new T-1 period swap at the beginning of period 2, without altering his payment stream. If, on the other hand, the quoted fixed rate had fallen to c’ at the beginning of period 2, then the floating-rate payor (= fixed-rate receiver) would only be able to replace the original swap with one that paid lower fixed payments, that is, the counterparty of the country has suffered an unrealized loss. This loss would be realized if the country were to default on the swap agreement at the beginning of period 2.22 Suppose, for example, an indebted developing country enters into an interest rate swap agreement with the bank under which the country pays 9.5 percent fixed interest on $100 million of notional principal for five years, while the bank pays LIBOR on the same notional $100 million for five years. Assume that at the beginning of year 2 the fixed interest rate swap rate on new four-year swaps has fallen to 8.5 percent. If the country defaults on its payment obligation, the bank will have to accept 8.5 percent fixed payments in return for LIBOR payments if it wants to replace the swap. Thus the bank will have lost 1 percent of $100 million for 4 years. If instead the fixed swap rate increases to 10.5 percent, a default by the country will not expose the bank to any losses. In this case, it can receive 10.5 percent fixed for its LIBOR payment. Potential losses are determined by the change in the fixed swap rate and not by its level, and no loss of principal is involved in a default on a swap contract. Thus, the credit risk on a medium-term swap contract is less than that of a loan contract of same principal. The potential losses over the period of the swap contract are a measure of the total credit exposure incurred by the counterparties. In order to determine the size of such exposure, it is necessary to determine the market value of swaps. The market value of the swap to the bank at the beginning of the second year is equal to the loss it sustains if the swap agreement became void through a default of the country. The replacement cost of a swap is equal to the market value or zero, whichever is larger. The next section produces a method for valuing swaps.

Pricing Interest Rate Swaps

By market convention swap rates are quoted as the internal rate of return of the fixed payment stream of the swap against the floating index flat. For example, a ten-year interest rate swap might be quoted to a fixed-rate payor as “Treasury yield curve plus 70 basis points against six-month LIBOR.”23 If the current rate on ten-year U.S. Treasury bonds is 8.8 percent, then the fixed rate payor of such a swap with notional principal of $100 million makes fixed semiannual payments of $4.75 million for ten years. He receives in return six-month LIBOR flat for ten years, for example, $4.25 million in the first six-month of the contract if LIBOR is currently 8.5 percent.

Thus the swap market determines the swap rate for swaps of given maturities rather than swap prices.24 Once the swap rate is known, that is, once the fixed payment stream is known, the market value of the swap can be computed.25 The market value of the interest rate swap for the party receiving fixed payments is equal to the market value of the incoming fixed-payment stream less the market value of the outgoing floating-payment stream. It is convenient in this context to view a swap as an exchange of two hypothetical securities, that is, the fixed-rate payor sells a fixed-rate bond priced at par to the floating-rate payor who sells a floating-rate LIBOR note priced at par of equal maturity to the fixed-rate payor.26 Since the notional principal amount of the swap is equal to the par amount of both hypothetical securities, there will be no net cash flows involving principal. The problem of determining the market value of a swap that has T fixed-rate payment periods left has then been transformed into one of finding the market value of these two hypothetical securities. The market value of the swap is the difference between the present value of the fixed rate payments and the present value of the floating rate payments.

A swap agreement entered into at the current swap rate27 is called a Par Swap, in this case the present value of the fixed payments and the present value of floating payments are both equal to the par value of underlying notional fixed- and floating-rate securities and the market value of the swap is zero.

The market value of the outstanding swap with a remaining maturity of T payment periods changes with variations in the quoted swap rate for new swaps of T period maturity. For example, an increase in the five-year swap rate implies that the swap contracted earlier, with a remaining time to maturity of five years, attains a positive market value from the point of view of the fixed-rate payor and an equal negative value from the point of view of the floating-rate payor.

The present value of the fixed payment stream is given by28



  • T = number of fixed-rate payment dates left;

  • q = number of fixed-rate payment dates per year;

  • F = notional amount of swap;

  • c = fixed-rate coupon for the swap in percent;

  • Zt = annualized zero-coupon equivalent rate for fixed rate payment date t; and

  • Kt = number of days until the fixed rate payment date t divided by 360.

The hypothetical floating rate note is valued at par at the next payment date, hence its price is the sum of the present value of the next payment plus the par value, that is,



  • n = number of days in the interest period of the floating note;

  • r = current floating rate index in percent.

The rates Zt used to discount future payments are zero-coupon rates derived from the U.S. Treasury yield curve (Appendix I) rather than current swap rates, which are yields to maturity or internal rates of return on swaps entered now. The reason is that a swap with a fixed rate different from the current market swap rate (off-market swap) has cash flows different from the current par swap and hence has a different internal rate of return than the current par swap. The present value of the off-market swap will thus depend on which internal rate of return (IRR) is used. Zero-coupon rates on the other hand are independent of the fixed rate of the swap and hence they are used to discount the fixed payments of the off-market swap.29

The value to the fixed-rate receiver of a swap contract with T payment periods until maturity is, therefore, equal to


Any change in the U.S. Treasury yield curve will induce changes in the zero coupon discount factors and hence the value of the swap will change. For example, an upward shift in the Treasury yield curve would increase the value of the swap to the fixed rate payor since PFixed decreases by more than PFloat.30

Since the country is not assumed to be free of default risk, the bank counterparty in the swap contract will not use the risk-free zero-coupon discount rates to determine the value of its swap, but instead will add a risk premium to the discount rates. Hence, in order to enter into such a swap, the country will have to pay a swap rate that reflects its default risk. Once the bank has determined the discount rates it will use to discount the uncertain fixed-rate payment stream from the country it can then determine the swap rate and a new swap rate can be found by setting the initial market value of the swap equal to zero, that is,



  • dt are the risk premia added to t period risk-free zero coupon discount rates; and

  • c̄ is the swap rate payable by the country with default risk.

Marking-to-Market of Swap Contracts

In order to find a way to reduce credit risk in swap contracts, we first examine how the futures market has dealt with credit risk. The credit risk associated with the obligation to make future delivery under futures contracts has successfully been minimized through institutional features, such as daily resettlement, margin requirements, and futures clearinghouses. Any gains or losses that arise on the futures contract because of changes in the price of the contract are realized the next morning through cash settlements among the contracting parties, and the futures price is then marked-to-market.31 Thus the performance period has been reduced to one day. In addition, market participants are required to post margins in the form of a performance bond, related to the estimated volatility of intraday futures prices, to cover any intraday losses. Thus the incentive to renege on the futures contract has been virtually eliminated. In addition, a clearinghouse interposes itself between transacting parties in all contracts, such that all contracts are with the clearinghouse as counterparty, which further reduces the risk of nonperformance. The homogenous nature of the futures contract and the bringing together of buyers and sellers in an organized futures exchange has resulted in a very liquid futures market.32 Generally, the longer the performance period, the greater the probability that swap rates change in such a way as to produce capital gains for the bank counterparty and the greater the credit risk. Hence, credit risk can be reduced by reducing the performance period.

The identification of the unrealized gains and losses occurring in swap contracts with changes in the swap rate makes it possible to design a similar mechanism of transferring the change in the swap’s value from the losers to the gainers followed by a marking-to-market of the swap rate, as a way to reduce the credit risk of the swap contract. By making such transfers of the heretofore unrealized changes in the value of the swap contract at the beginning of each coupon period and by resetting the original swap rate to the prevailing market rate, we can reduce the size of losses to changes in the swap’s market value occurring during a single coupon period.33

Consider for example (Table 2) a two-year swap of $500 million notional principal priced at 9.8 percent against six-month LIBOR flat with fixed-rate payment dates made to coincide with the floating-rate payment dates. At the end of the first half year, the fixed payor pays interest of $24.5 million34 to the floating-rate payor. In addition, if the swap rate for a nine semester swap at the end of the first semester has moved from 9.8 to 10.4 percent then the fixed-rate payor has an unrealized capital gain of (0.06) × (500,000,000) for nine semesters, discounted at the new swap rate of 10.4 percent, that is, of $10,567,000.35 Thus the country would receive this amount from its counterparty. The net fixed-rate payments would then amount to $13,933,000. If, instead, the swap rate for nine semester swaps at the beginning of the reset period were below the original coupon rate of 9.8 percent, then the fixed-rate payor would make a payment to the fixed-rate receiver. In either case, once such payments have been made the swap’s fixed coupon rate is set equal to the new swap market rate, that is, to 10.4 percent in the example. The payment made at the time of the marking-to-market of the swap and the adjustment in the fixed coupon cancel out in present value terms, so that the effective fixed rate on the swap (the internal rate of return on all payments) is equal to the original coupon.

Table 2.

Marking-to-Market of Interest Rate Swaps

(Five-year swap, semiannual, 9.8 percent fixed payment)

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Amounts in brackets are resettlement payments to fixed-rate payor from floating-rate payor, while amounts without brackets are resettlement payments from fixed-rate payor to floating-rate payor.

The shorter the performance period, the smaller the expected changes in swap rates during the period and the smaller the changes in market value from one settlement date to the next. For example, Table 2 is based on a semiannual settlement, while Table 3 is based on quarterly resettlement. It can be seen that the marked-to-market settlements are smaller when paid quarterly, that is, the credit risk is smaller, the smaller the performance period. It is theoretically possible to reduce the performance period to a single day, as is the case in the futures markets. The practical difficulty with shortening the performance period below three months is that then fixed-rate payments have to be made more than four times annually, and interest payment frequency higher than four times a year annum has been resisted by the market participants for administrative reasons.

Table 3.

Marking-to-Market of Interest Rate Swaps

(Five-year swap, quarterly (30/360), 9.8 percent fixed payment)

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Amounts in brackets are resettlement payments to fixed-rate payor from floating-rate payor, while amounts without brackets are resettlement payments from fixed-rate payor to floating-rate payor.

Thus, in swaps with such mark-to-market provision only the risk of not receiving the net fixed interest payment due in the current coupon period remains. Such risk could be removed by a collateral deposit or performance bond similar to that required in the futures market. For example, for a five-year swap rate of 9 percent and LIBOR of 8 percent, the maximum interest payment lost could be 25 basis points of principal36 plus, for example, another 10 basis points to account for intra-quarter volatility of swap rates. Thus, a performance bond of 50 basis points of principal would make such five-year swap contract almost riskless.37

III. Some Remaining Problems

The practice of periodic resettlement and marking-to-market of swap rates exposes the indebted developing country to potentially large variations in cash flows. However, such flows occur in the opposite direction of interest rate movements. As rates rise, the country receives payments, while a decline in rates leads to payments by the country. It is thus necessary to put in place an active system of management of cash-flows over the term of the hedge. The marked-to-market settlements in Tables 2 and 3 are subtracted from the fixed interest payments if the swap rate has risen (that is, the value of the swap to the fixed-rate payor had become positive) or added to fixed interest payments if the swap rate has declined (i.e., the value of the swap to the floating-rate payor has become positive). The resulting net fixed swap payments flow to be made by the country has, however, an interest rate of return equal to the initial swap rate (9.80 in the example in Tables 2 and 3). Thus, although the payments by the country to the swap counterparty, that is, the floating-rate payor, have become variable, the internal rate of return of the payments remains unchanged. It will generally not be possible for indebted developing countries to use the expected payments by the floating-rate payor as collateral for borrowing to finance the marked-to-market settlement payments. An early default by the country would result in a loss of floating-rate payments by the floating-rate payor since future payments from the floating rate payor are made only as long as the fixed-rate payor is not in default.

Since indebted developing countries have generally made interest payments on their external obligations there would appear to be scope for multilateral lending agencies to facilitate such technical problems associated with the cash-flow requirement of converting floating rate payment into fixed-rate payment through an interest rate swap.

IV. Conclusions

In this paper we first showed that the interest rate swap is the most promising candidate among the currently available interest rate risk management tools that would satisfy the special requirements of indebted developing countries. Since collateralization of swaps is rejected because of lack of pledgeable resources, we propose to shorten the performance period to coincide with the coupon period by resettling the swap contract at interest payment dates and marking the swap rate to market. The intra-coupon period performance risk can be eliminated through a performance bond. Since this marking-to-market procedure can easily be added to the conventional swap contract, it could allow indebted developing countries access to a deep and flexible market for turning floating into fixed payments over the medium term.

The main drawback of this method is the cash flow requirements inherent in the procedure.38 However, the internal rate of return on net fixed-rate payments remains equal to the initial swap rate. Furthermore, while the periodic resettlement tends to raise and lower the fixed-rate payments in some periods, it does so in the opposite direction of the movement in rates. For instance, an increase in the long rate would result in payments being made by the floating-rate payor to the country, while a decrease in the long rate would result in payments from the country to the floating-rate payor.

A second drawback is the administrative cost of marking swap contracts to markets. Estimates suggest, however, that such costs would be unlikely to add more than 1 basis point to market swap rates on notional principals in excess of $100 million. It is also possible that if the marking-to-market of interest rate swaps is accepted by the market, the resulting elimination of credit risk and a standardization of contract could lead to an exchange traded contract much like the future contract.

The introduction of a marked-to-market swap contract would allow indebted developing countries to extend the length of the coupon period of their existing external obligation into the medium term at a modest spread above the U.S. Treasury yield curve.39

APPENDIX I Conversions of Yields-to-Maturity to Zero-Coupon-Rates

This appendix shows how the yield-to-maturity of an annual-coupon-paying bond can be converted to corresponding zero-coupon-yields. The correspondence of a yield-to-maturity and zero-coupon yield is based on the equivalence of the two methods of determining the market price of a T-period coupon-paying bond:


PT = price of a T period bond;

F = face value;

cT = coupon rate on T-price bond;

rT = yield-to-maturity on T period bond; and

pt = zero coupon rate for discounting payments received in period t.

Let the bond be issued at par, then


After substituting (7) into (6), we get


Equation (8) can be solved iteratively for pT by letting T go from 1 to the desired maturity. For example, T = 1 implies that p1 = r1, that is, in the one-period case the yield-to-maturity is equal to the zero-coupon discount rate. With t = 2 and p1 = r1, we have from equation (8)


which can be solved for ρ2 as a function of c1 and c2. This process continues until the desired maturity T, at which point the procedure has computed ρ1, ρ2, and ρt as the zero-coupon rates.


Counterparty: The other party to a contract. For exchange-traded futures and options contracts, the counterparty is usually the exchange itself (an exception is LIFFE, where the broker plays this role). For OTC instruments, the counter-party is generally a financial intermediary, such as a major money-center bank, an investment or merchant bank, or a securities company.

Counterparty Risk: The risk that the other party to a contract will not fulfill the terms of the contract. This risk is avoided through the clearinghouse system for exchange-traded instruments; however, it is a relevant source of risk for OTC instruments, such as forward agreements, interest-rate caps, floors and collars, and interest rate or currency swaps.

Credit Risk: Risk associated with the possibility that the other party to a financial contract will be unwilling or unable to fulfill the terms of the contract. Credit risk is distinguished from the risks associated with changes in prices, interest rates, or exchange rates (see also Counterparty Risk).

Currency Swap: A transaction in which two counterparties exchange specific amounts of two different currencies at the outset and repay over time according to a predetermined schedule that reflects interest payments and possibly amortization of principal. The payment flows in currency swaps (in which payments are based on fixed interest rates in each currency) are generally like those associated with a combination of spot and forward currency transactions.

Delivery: There are three types of delivery on futures contracts: “current”—delivery during the present month; “nearby”—delivery during the nearest active month; “distant”—delivery in a month further off.

Delivery Date: Date on which the commodity must be delivered to fulfill the terms of the contract.

Delivery Price: Price fixed by clearinghouse at which futures deliveries are invoiced. Also price at which a commodities futures contract is settled when deliveries are made.

Forward Contract: A cash market transaction in which two parties agree to the purchase and sale of a commodity at some future time under such conditions as the two agree. In contrast to a futures contract, the terms of a forward contract are not standardized; a forward contract is not transferable and usually can be cancelled only with the consent of the other party, which often must be obtained for consideration and other penalties. Also forward contracts are not traded on organized exchanges.

Forward Rate Agreement (FRA): An agreement between two parties wishing to protect themselves against a future movement in interest rates or exchange rates. In an interest-rate FRA, the two parties agree on an interest rate for a specified period from a specified future settlement date based on an agreed principal amount. No commitment is made by either party to lend or borrow the principal amount; their right (obligation) is only to receive (pay) the difference between the agreed and actual interest rates at settlement. Similar agreements can be made with respect to an exchange rate.

Futures Contract: An exchange-traded contract generally calling for delivery of a specified amount of a particular grade of commodity or financial instrument at a fixed date in the future. Contracts are highly standardized and traders need only agree on the price and number of contacts traded. Traders’ positions are maintained at the exchange’s clearinghouse, which becomes a counterparty to each trade once the trade has been cleared at the end of each day’s trading session. Members holding positions at the clearinghouse must post margin, which is marked-to-market daily. Most trades are unwound before delivery. The interposition of the clearinghouse facilitates the unwinding since a trader need not find his original counterparty, but may arrange an offsetting position with any trader on the exchange (see Margin).

Interest Rate Cap: An option-like feature for which the buyer pays a fee or premium to obtain protection against a rise in a particular interest rate above a certain level. For example, an interest rate cap may cover a specified principal amount of a loan over a designated time period, such as a calendar quarter. If the covered interest rate rises above the rate ceiling, the seller of the rate cap pays the purchaser an amount of money equal to the average rate differential times the principal amount times one-quarter.

Interest Rate Swap: A transaction in which two counterparties exchange interest payment streams of differing character based on an underlying notional principal amount. The three main types are coupon swaps (fixed rate to floating rate in the same currency), basis swaps (one floating rate index to another floating rate index in the same currency), and cross-currency interest rate swaps (fixed rate in one currency to floating rate in another).

Long Position: (1) In the futures market, the position of a trader on the buying side of an open futures contract; (2) in the options market, the position of a trader who has purchased an option regardless of whether it is a put or a call. A participant with a long call-option position can profit from a rise in the price of the underlying instrument while a trader with a long put option can profit from a fall in the price of the underlying instrument.

Maintenance Margin: The minimum amount which must remain in the margin account after any market losses are deducted from the initial margin. Once the account declines to the maintenance level, the broker will issue a margin call, a request that the client restore the account to its original level. Should the client refuse or default, the position may be closed out by the broker.

Margin: An amount of money deposited by both buyers and sellers for futures contracts to ensure performance of the terms of the contract, that is, the delivery or taking of delivery of the commodity or the cancellation of the position by a subsequent offsetting trade at such price as can be attained. Margin in futures markets is not a payment of equity or down payment on the commodity itself but rather is in the nature of a performance bond or security deposit (see Initial Margin and Maintenance Margin).

Margin Call: A commodity broker’s request to a client for additional funds to secure the original deposits. Margin that must be posted in response to a margin call is known as Variation Margin.

Notional Principal: A hypothetical amount on which swap payments are based. The notional principal in an interest rate swap is never paid or received.

Open Interest: The total number of futures contracts of a given commodity which have not yet been offset by opposite futures transactions nor fulfilled by delivery of the commodity; the total number of open transactions. Each open transaction has a buyer and a seller, but for calculation of open interest, only one side of the contract is counted.

Option: The contractual right, but not the obligation, to buy or sell a specified amount of a given financial instrument at a fixed price before or at a designated future date. A call option confers on the holder the right to buy the financial instrument. A put option involves the right to sell the financial instrument.

OTC Market (Over-The-Counter Market): Trading in financial instruments transacted off organized exchanges. Generally the parties must negotiate all details of the transactions, or agree to certain simplifying market conventions. In most cases, OTC market transactions are negotiated over the telephone. OTC trading includes transactions among market-makers and between market-makers and their customers. Firms mutually determine their trading partners on a bilateral basis.

Position: A market commitment. For example, one who has bought futures contracts is said to have a long position, and conversely, a seller of futures contracts is said to have a short position.

Settlement Price: The price of the financial instrument underlying the option contract at the time the contract is exercised. Where necessary, option contracts specify objective standards for determining the settlement price.

Short Position: (1) In the futures market, the position of a trader on the selling side of an open futures contract; and (2) in the options market, the position of a trader who has sold or written an option regardless of whether it is a put or a call. The writer’s maximum potential profit is the premium received.

Stack Hedge: A futures hedging strategy that involves taking a large position in an existing contract, and subsequently rolling over part of this position into a later contract month, possibly repeating this procedure several times. This strategy may be used to hedge risks associated with a series of payments or receipts, particularly where these are to occur at dates for which futures contracts are nonexistent or illiquid (see also Strip, Liquidity).

Strip: (1) A futures position established by taking the same (long or short) position in a futures contract for a series of delivery dates. This strategy may be used to hedge risk associated with a series of payments or receipts; (2) An options straddle position consisting of the purchase of more puts than calls although all have the same exercise date and exercise price. While the trader expects an increase in price volatility, there is also the expectation that the price of the underlying instrument is more likely to fall than to rise.

Underlying Instrument: The designated financial instruments which must be delivered in completion of an option contract or a futures contract. For example, the underlying instrument may be fixed-income securities, foreign exchange, equities, or futures contracts (in the case of futures option).

Volatility: The price “variability” of the instrument underlying an option contract, and defined as the standard deviation in the logarithm of the price of the underlying instrument expressed at an annual rate. Expected volatility is a variable used in pricing options (see Standard Deviation).


  • Bank for International Settlements, Recent Innovations in International Banking (Basel: BIS, 1986).

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  • International Monetary Fund, “Managing Financial Risks in Indebted Developing Countries” (forthcoming).

  • Kopprasch, R., and others, The Interest Rate Swap Market: Yield Mathematics Terminology and Conventions (New York: Salomon Brothers, 1988).

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  • Miller, M., “Financial Innovation: The Last Twenty Years and the Next,” Journal of Financial and Quantitative Analysis (Seattle, Washington), Vol. 21, No. 4 (December 1986).

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  • Stiglitz, Joseph E., and Andrew Weiss, “Credit Rationing in Markets with Imperfect Information,” American Economic Review, Vol. 71 (June 1981).

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  • Watson, Maxwell, and others, International Capital Markets, World Economic and Financial Surveys (Washington: International Monetary Fund, 1988).

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Mr. Folkerts-Landau is the Assistant Division Chief of the Financial Studies Division of the Research Department. He is a graduate of Harvard University and holds a doctorate from Princeton University. He was an Assistant Professor of Economics and Finance in the Graduate School of Business, University of Chicago, before joining the International Monetary Fund.


Financial hedging instruments (financial futures, forward, options and swap contracts) are contingent contracts entitling holders to payments that are conditional on the outcome of future interest rates.


The LIBOR increase of about 3 percentage points over the past two years has resulted in increases in interest payments by indebted developing countries in excess of $5 billion annually.


As has been noted elsewhere (e.g., Stiglitz and Weiss (1981)), some financial markets, in particular the market for bank loans and interbank funds, exclude borrowers whose perceived credit risk exceeds a certain level, rather than demand a correspondingly higher risk premium. Such credit rationing behavior is readily apparent not only in international bank lending to developing countries but also in the markets for hedging instruments that expose bank intermediaries to credit risk (see Folkerts-Landau (1985)). The direct debt markets appear to be better able to price credit risk, as, for example, in the so-called noninvestment grade, that is, junk bond market.


Indeed, such limitations have led to the inclusion of a short-term international interest rate index as contingent variable in the Fund’s recently established compensatory and contingent financing facility.


See Managing Financial Risks in Indebted Developing Countries, IMF Occasional Paper, 1989 (forthcoming).


For a theoretical discussion of the general benefits of reduced risk for developing countries, see R. Brignoli and L. Seigel, “The Role of Noise in LDC Growth,” presented at Roundtable Conference on Trends in International Capital Markets, Oxford, 1988.


This recontracting and resettlement methodology has been successfully employed to eliminate the credit risk from short-dated futures contracts (see below).


Estimate provided by the International Swap Dealers Association. Notional principal refers to the notional amount on which swap payments are based. The notional principal in an interest rate swap is never paid or received.


The one notable exception has been Chile, which in 1988 undertook a limited interest rate risk management operation involving the sale of Eurodollar futures contracts to hedge against increases in LIBOR before the next interest rate reset date.


The coupon period is the period over which the interest payable on the liability remains fixed.


The predominant example of interest rate forward contracts is the forward rate agreement (FRA), a contract in which two counterparties agree on the interest rate to be paid on notional deposits of specified maturity at a specified future date. The market for FRAs has grown rapidly and is now estimated to exceed $100 billion outstanding in notional principal. Maturities of up to six months for delivery up to one year are most common.


If, for example, the contracted interest rate on six-month funds is p and the spot rate at the delivery date is r < p, then the potential default loss for the counterparty is (p - r)F/2, where F is the nominal size of the contract. (The contract is usually cash settled, that is, by paying the interest differential without principal payments.) Hence, the longer the time to delivery and the more volatile the underlying interest rate the greater the likelihood that r differs from p.


If one of the parties in an interest rate swap fails to fulfill its obligations under the swap contract, then the other party is released from making its payments.


It is estimated that in excess of $750 billion of LIBOR caps are outstanding. Available maturities run through ten years with most liquidity occurring for caps between one to five years of maturity.


Conventional options pricing models can be used to determine the size of the premium.


The Eurodollar futures market has grown rapidly to reach an open interest in excess of 250,000 contracts (contract size is $1 million) and a daily trading volume in excess of 80,000 contracts. The contract for the future delivery of U.S. Treasury bills is nearly as successful in terms of volume traded and open interest as the Eurodollar contract, but it does not allow a perfect hedge for the LIBOR index since the Treasury bill-LIBOR spread is not constant.


A strip hedge covering one year consists of selling three-month Eurodollar contracts for delivery at the end of each of the four quarters. A stack hedge covering one year involves selling four times as many three-month futures contracts as the amount tobe hedged. At the end of the first quarter, that is, the first LIBOR reset date, one quarter of the stack is closed out while the rest rolled over into the most nearby three-month contract. This procedure is repeated at each quarterly LIBOR reset date until the entire position is closed out at the end of the year. Prices for futures contracts traded at the end of each quarter are uncertain, however, and thus it is not possible to construct a precise hedge. In particular, the term structure of interest rates may twist, with short-term rates remaining relatively stable while medium- and longer-term rates rise. See International Monetary Fund (1989) for example of futures hedges.


An important theoretical question remains unresolved concerning the preference of lenders in such markets to ration access rather than to charge risk premia in accordance with their perception of the credit risk of countries.


A wide variety of swap structures exists. We shall confine our discussion to the generic swap, in which fixed payments are exchanged for floating payments, on the same day, in the same currencies. See Kopprasch and others (1988).


We assume for the time being that the country makes the interest payment due at the beginning of period 1 and then announces its withdrawal from the swap agreement.


For example, in January 1989 quotations for U.S. dollar interest rate swaps were: two-year U.S. Treasury + (56–61); three-year U.S. Treasury + (57–62); five-year U.S. Treasury + (58–63); and ten-year U.S. Treasury + (64–70).


Swap rates are determined by demand and supply in a screen-based market encompassing most larger banks and other financial institutions.


In contrast, market makers for U.S. Government bonds quote the price of a given bond rather than its yields, which can be computed once the price is known.


It is assumed that the payment dates of the fixed- and floating-rate payments coincide with the floating-rate reset dates.


The quoted swap rate is equivalent to the yield to maturity or IRR of an underlying hypothetical fixed-rate security with the same coupon.


The time convention in the interest rate calculations used here is 30/360.


This valuation problem is thus strictly analogous to valuing a certain stream of fixed payments made by risk-free payor to a risk-free borrower. In this case, each payment would be discounted by the appropriate risk-free zero coupon rate and the value of the stream would be equal to the sum of the terms.


The longer maturity of the hypothetical fixed-rate security implies that its present value changes by more with changes in interest rates than that of the floating-rate security.


For example, assume a country sells 1,000 contracts ($1 million per contract) for delivery of three-month Eurodollar deposits at a specified future date at 92 cents per dollar. If on the next day the futures interest rate on the three-month Eurodollar deposits has decreased by five basis points, that is, the price of the contract has risen by five basis points, then the country will have suffered a $125,000 loss on its short futures position. The resettlement procedure provided for the $125,000 to be paid to the holder of the contracts and for the interest rate at which the Eurodollar deposits will be supplied is to be adjusted upward by five basis points.


The introduction of exchange-traded financial futures should be regarded as one of the most successful financial innovations of the past decade; see Miller (1986).


We assume that interest payment remains current up to the time the swap contract is declared nonperforming.


500,000,000 × 0.098/2 = 24,500,000.




One percent over one year or 25 basis points per quarter.


It is apparent from Table 2 and from equation (1) that changes in swap rates which occur early result in larger marked-to-market settlements than changes of the same magnitude occurring later into the contract.


Such cash flows are less than would be the case under comparable interest rate hedge constructed with futures contracts.


See footnote 25.